Stability analysis of a general toeplitz systems solver

This paper concerns a special type of eddy-current sensor in the form of inductive loops. Such sensors are applied in the measuring systems classifying road vehicles. They usually have a rectangular shape with dimensions of 1 × 2 m, and are installed under the surface of the traffic lane.The wide Point Spread Function (PSF) of such sensors causes the information on chassis geometry, contained in the measurement signal, to be strongly averaged. This significantly limits the effectiveness of the vehicle classification. Restoration of the chassis shape, by solving the inverse problem (deconvolution), is also difficult due to the fact that it is ill-conditioned.An original approach to solving this problem is presented in this paper. It is a hardware-based solution and involves the use of inductive loops with an asymmetrical PSF. Laboratory experiments and simulation tests, conducted with models of an inductive loop, confirmed the effectiveness of the proposed solution. In this case, the principle applies that the higher the level of sensor spatial asymmetry, the greater the effectiveness of the deconvolution algorithm.

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“…It is always, however, a matrix with a Toeplitz structure [11,12]. In the most general case, it takes the form of Equation (7).…”

Section: Convolution Matrixmentioning

confidence: 99%

Eddy-Current Sensors with Asymmetrical Point Spread Function

Gajda

Stencel

2016

Sensors

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“…In the first step, the linear system solving is based on the Cholesky factorization of the symmetrical matrix Z. The complexity is O(K 3 ), but could be reduced to O(K 2 ) by using the Hankel property of Z [see Bojanczyk et al (1995) for instance]. The roots of q y min (α) are then calculated with Matlab function "roots", which builds the companion matrix of q y min (α) then finds its eigenvalues with a Q R factorization method.…”

Section: K -Product Algorithmmentioning

confidence: 99%

A global algorithm to estimate the expectations of the components of an observed univariate mixture

Paul

Terré

Fety

2007

ADAC

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This paper deals with the unsupervised classification of univariate observations. Given a set of observations originating from a K -component mixture, we focus on the estimation of the component expectations. We propose an algorithm based on the minimization of the "K -product" (KP) criterion we introduced in a previous work. We show that the global minimum of this criterion can be reached by first solving a linear system then calculating the roots of some polynomial of order K . The KP global minimum provides a first raw estimate of the component expectations, then a nearest-neighbour classification enables to refine this estimation. Our method's relevance is finally illustrated through simulations of various mixtures. When the mixture components do not strongly overlap, the KP algorithm provides better estimates than the Expectation-Maximization algorithm.

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“…In many cases, solving (1) by means of the solution of the normal equations is not recommended because the condition number κ(T T T ) can be as large as κ(T ) 2 [20,Section 5.3]. However, this method can be used in the Toeplitz case because, as has been proved in [6] using the results in [8] and [7], the computed triangular factorR satisfies…”

Section: Solution Of the Normal Equationsmentioning

confidence: 99%

An Efficient Parallel Algorithm to Solve Block?Toeplitz Systems

2005

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Abstract. In this paper, we present an efficient parallel algorithm to solve Toeplitz-block and block-Toeplitz systems in distributed memory multicomputers. This algorithm parallelizes the Generalized Schur Algorithm to obtain the semi-normal equations. Our parallel implementation reduces the communication cost and optimizes the memory access. The experimental analysis on a cluster of personal computers shows the scalability of the implementation. The algorithm is portable because it is based on standard tools and libraries, such as ScaLAPACK and MPI.

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Stability analysis of a general toeplitz systems solver

Cited by 20 publications

References 74 publications

Eddy-Current Sensors with Asymmetrical Point Spread Function

Eddy-Current Sensors with Asymmetrical Point Spread Function

A global algorithm to estimate the expectations of the components of an observed univariate mixture

An Efficient Parallel Algorithm to Solve Block?Toeplitz Systems

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